# Google Sheets BETADIST Function: Syntax, Examples & Tips - URL: https://betteranalyst.com/google-sheets/betadist-function - Author: Better Analyst Formula Bot is now Better Analyst—same account, more powerful analysis.Formula Bot is now Better Analyst—same account and workflows, with more powerful analysis, dashboards, and automation. [Learn what changed](https://betteranalyst.com/formula-bot-is-now-better-analyst) Returns the cumulative probability of the beta distribution at a given value. ``` =BETADIST(value, alpha, beta, [lower_bound], [upper_bound]) ``` Generate FormulaExplain Formula One free generation or explanation per browser, shared across Excel and Google Sheets. Account usage limits apply afterward. Describe the BETADIST you need in plain EnglishGenerate Formula ## Parameters | Parameter | Required | Description | | - | - | - | | **value** | Yes | The point at which to evaluate the distribution. Must lie between **lower\_bound** and **upper\_bound**. | | **alpha** | Yes | The first shape parameter. Must be greater than 0. | | **beta** | Yes | The second shape parameter. Must be greater than 0. | | **lower\_bound** | No | The lower end of the interval. Defaults to 0. | | **upper\_bound** | No | The upper end of the interval. Defaults to 1. | ## What Is BETADIST? BETADIST evaluates the cumulative beta distribution, a family of probability distributions defined on a bounded interval (by default from 0 to 1). Because it lives between two limits, the beta distribution is a natural model for proportions and rates: conversion rates, completion percentages, the share of time a task takes up, or an uncertain probability. Two shape parameters, **alpha** and **beta**, control its form. Equal values give a symmetric curve centred on the middle of the interval. A larger alpha pushes the bulk of the curve towards the upper bound; a larger beta pushes it towards the lower bound. When both are 1, the distribution is flat (uniform). BETADIST is a legacy function kept for compatibility with older spreadsheets. Its modern equivalent is **BETA.DIST**. `=BETADIST(x, a, b)` gives the same answer as `=BETA.DIST(x, a, b, TRUE)`. BETA.DIST also lets you return the density instead of the cumulative probability by setting `cumulative` to FALSE, so prefer it in new work. ## How BETADIST Works BETADIST always returns a cumulative probability: the chance that a beta-distributed variable is less than or equal to **value**. The answer is a number between 0 and 1. It cannot return the density (the height of the curve); for that, use `BETA.DIST(value, alpha, beta, FALSE)`. Densities are not probabilities and can be greater than 1. If your quantity runs on a scale other than 0 to 1, supply **lower\_bound** and **upper\_bound**. Google Sheets rescales **value** into that interval before calculating. ## Basic Examples ### Cumulative probability ``` =BETADIST(0.5, 2, 3) ``` Returns 0.6875: with alpha 2 and beta 3, there is a 68.75% chance the variable is at or below 0.5. ### Density at a point (modern function) ``` =BETA.DIST(0.5, 2, 3, FALSE) ``` Returns 1.5, the height of the curve at 0.5. BETADIST cannot do this. ### Custom bounds ``` =BETADIST(50, 2, 3, 0, 100) ``` Same shape on a 0–100 scale. Returns 0.6875, because 50 sits halfway along the interval. ### Probability between two values ``` =BETADIST(0.6, 8, 12) - BETADIST(0.3, 8, 12) ``` The chance that the variable falls between 0.3 and 0.6. ## Using BETADIST for Conversion Rates A common Bayesian shortcut: after observing *s* successes and *f* failures, starting from a flat prior, the conversion rate can be modelled as Beta(s + 1, f + 1). With 40 conversions out of 400 visits: ``` =1 - BETADIST(0.12, 41, 361) ``` estimates the probability that the true conversion rate is above 12%. ## Common Use Cases - **A/B testing**: probability that a conversion rate exceeds a target - **Project management**: PERT-style estimates of task duration between a minimum and maximum - **Quality**: modelling the proportion of defective items - **Risk analysis**: uncertain percentages in simulations ## Common Errors - **#NUM!**: alpha or beta is zero or negative, or **value** is outside the bounds. - **#NUM! from bounds**: **lower\_bound** is not less than **upper\_bound**. - **#VALUE!**: An argument is text that cannot be read as a number. - **Passing a cumulative flag**: BETADIST has no `cumulative` argument. A fourth argument is read as **lower\_bound**, which gives unexpected results. If you need that flag, switch to BETA.DIST. ## Tips and Best Practices - To go the other way, from a probability back to a value, use [BETAINV](https://betteranalyst.com/google-sheets/betainv-function). - The mean of a standard beta distribution is alpha ÷ (alpha + beta). Use this to sanity-check your parameters. - Plotting the density over a column of values from 0 to 1 is a quick way to see the shape you have chosen. ## Related Functions - [BETAINV](https://betteranalyst.com/google-sheets/betainv-function): inverse of the cumulative beta distribution - [BINOMDIST](https://betteranalyst.com/google-sheets/binomdist-function): probabilities for counts of successes - [AVERAGE](https://betteranalyst.com/google-sheets/average-function): the mean of a data set - [ROUND](https://betteranalyst.com/google-sheets/round-function): tidy up probability results - [IF](https://betteranalyst.com/google-sheets/if-function): turn a probability into a decision ## Example use case A growth analyst sees 40 sign-ups from 400 visitors on a new landing page. Using =1-BETADIST(0.12, 41, 361), they estimate the probability that the page's true conversion rate is above the 12% target. ## Need more help with Google Sheets formulas? 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